Chaotic dynamics are at the center of multiple studies to perfect encrypted communication systems. Indeed, the particular time evolution nature of chaotic signals constitutes the fundamentals of their application to secure telecommunications. The pseudo random signal constitutes the carrier wave for the communication. The information coded on the carrier wave can be extracted with knowledge of the system dynamic evolution law. This evolution law consists of a second-order delay differential equation in which intervene the various parameters of the physical system setup. The set of precise parameter values forms the key, in a cryptographic sense, of the encrypted transmission. This thesis work presents the implementation of an experimental encryption system using chaos. The optical intensity of the emitter fluctuates chaotically and serves as carrier wave. A message of small amplitude, hidden inside the fluctuations of the carrier wave, is extracted from the transmitted signal by a properly tuned receiver. The influence of the message modulation format on the communication quality both in the back to back case and after propagation is investigated numerically.

The objective of this research is focused on two of the most important privacy-preserving techniques: privacy-preserving element matching protocols and privacy-preserving credential authentication protocols, where an element represents the information generated by users themselves and a credential represents a group membership assigned from an independent central authority (CA). The former is also known as private set intersection (PSI) protocol and the latter is also known as secret handshake (SH) protocol. In this dissertation, I present a general framework for design of efficient and secure PSI and SH protocols based on similar message exchange and computing procedures to confirm “commonality” of their exchanged information, while protecting the information from each other when the commonalty test fails. I propose to use the homomorphic randomization function (HRF) to meet the privacy-preserving requirements, i.e., common element/credential can be computed efficiently based on homomorphism of the function and uncommon element/credential are difficult to derive because of the randomization of the same function. Based on the general framework two new PSI protocols with linear computing and communication cost are proposed. The first protocol uses full homomorphic randomization function as the cryptographic basis and the second one uses partial homomorphic randomization function. Both of them achieve element confidentiality and private set intersection. A new SH protocol is also designed based on the framework, which achieves unlinkability with a reusable pair of credential and pseudonym and least number of bilinear mapping operations. I also propose to interlock the proposed PSI protocols and SH protocol to design new protocols with new security properties. When a PSI protocol is executed first and the matched elements are associated with the credentials in a following SH protocol, authenticity is guaranteed on matched elements. When a SH protocol is executed first and the verified credentials is used in a following PSI protocol, detection resistance and impersonation attack resistance are guaranteed on matching elements. The proposed PSI and SH protocols are implemented to provide privacy-preserving inquiry matching service (PPIM) for social networking applications and privacy-preserving correlation service (PAC) of network security alerts. PPIM allows online social consumers to find partners with matched inquiries and verified group memberships without exposing any information to unmatched parties. PAC allows independent network alert sources to find the common alerts without unveiling their local network information to each other.

Providing a security proof is always an important issue in the process of designing a cryptographic scheme or protocol. We often show the security of a cryptosystem via ¡§problem reduction.¡¨ In this thesis, lots of emphasis was put on the review of techniques for proving the security of cryptosystems. These techniques consist of Random Oracle Model and Forking Lemma. We also introduced some well-known cryptographic schemes which can be proved secure using these techniques. Then we offered a security proof of a blind signature scheme based on the one proposed by Fan. In the end, we made a comparison between our proof and the proof of another blind signature scheme provided by David Pointcheval and Jacques Stern. Some arguments and discussions about using the Random Oracle Model to prove the security of a cryptosystem were also included.

NTRU is a public key cryptosystem, which was first introduced in 1996. It is a ring-based cryptosystem and its security relies on the complexity of a well-known lattice problem, i.e. shortest vector problem (SVP). There is no efficient algorithm known to solve SVP exactly in arbitrary high dimensional lattices. However, approximate solutions to SVP can be found by lattice reduction algorithms. LLL is the first polynomial time algorithm that finds reasonable short vectors of a lattice. The best known attacks on the NTRU cryptosystem are lattice attacks. In these attacks, the lattice constructed by the public key of the system is used to find the private key. The target vector, which includes private key of the system is one of the short vectors of the NTRU lattice. In this thesis, we study NTRU cryptosystem and lattice attacks on NTRU. Also, we applied an attack to a small dimensional NTRU lattice.

A compact cryptographic processor with custom integrated cryptographic coprocessors is designed and implemented. The processor is mainly aimed for IPSec applications, which require intense processing power for cryptographic operations. In the present design, this processing power is achieved via the custom cryptographic coprocessors. These are an AES engine, a SHA-1 engine and a Montgomery modular multiplier, which are connected to the main processor core through a generic flexible interface. The processor core is fully compatible with Zylin Processor Unit (ZPU) instruction set, allowing the use of ZPU toolchain. A minimum set of required instructions is implemented in hardware, while the rest of the instructions are emulated in software. The functionality of the cryptographic processor and its suitability for IPSec applications are demonstrated through implementation of sample IPSec protocols in C-code, which is compiled into machine code and run on the processor. The resultant processor, together with the sample codes, presents a pilot platform for the demonstration of hardware/software co-design and performance evaluation of IPSec protocols and components.

In this thesis, we explore the pairing-based cryptography on elliptic curves from the theoretical and implementation point of view. In this respect, we first study so-called pairing-friendly elliptic curves used in pairing-based cryptography. We classify these curves according to their construction methods and study them in details. Inspired of the work of Koblitz and Menezes, we study the elliptic curves in the form $y^{2}=x^{3}-c$ over the prime field $F_{q}$ and compute explicitly the number of points $#E(mathbb{F}_{q})$. In particular, we show that the elliptic curve $y^{2}=x^{3}-1$ over $mathbb{F}_{q}$ for the primes $q$ of the form $27A^{2}+1$ has an embedding degree $k=1$ and belongs to Scott-Barreto families in our classification. Finally, we give examples of those primes $q$ for which the security level of the pairing-based cryptographic protocols on the curve $y^{2}=x^{3}-1$ over $mathbb{F}_{q}$ is equivalent to 128-, 192-, or 256-bit AES keys. From the implementation point of view, it is well-known that one of the most important part of the pairing computation is final exponentiation. In this respect, we show explicitly how the final exponentiation is related to the linear recurrence relations. In particular, this correspondence gives that finding an algoritm to compute final exponentiation is equivalent to finding an algorithm to compute the $m$-th term of the associated linear recurrence relation. Furthermore, we list all those work studied in the literature so far and point out how the associated linear recurrence computed efficiently.

The representation of field elements has a great impact on the performance of the finite field arithmetic. In this thesis, we give modified version of redundant representation which works for any finite fields of arbitrary characteristics to design arithmetic circuits with small complexity. Using our modified redundant representation, we improve many of the complexity values. We then propose new representations as an alternative way to represent finite fields of characteristic two by using Charlier and Hermite polynomials. We show that multiplication in these representations can be achieved with subquadratic space complexity. Charlier and Hermite representations enable us to find binomial, trinomial or quadranomial irreducible polynomials which allows us faster modular reduction over binary fields when there is no desirable such low weight irreducible polynomial in other representations. These representations are very interesting for the NIST and SEC recommended binary fields GF(2^{283}) and GF(2^{571}) since there is no optimal normal basis (ONB) for the corresponding extensions. It is also shown that in some cases the proposed representations have better space complexity even if there exists an ONB for the corresponding extension.

Due to the flush development of academic research, a great deal research results have been published in conference proceedings and journals. However, these articles need to be inspected by some professionals in specific fields. It is the most important that fairness must be guaranteed during the entire process of reviewing. Nevertheless, the privacy of reviewers may be leaked out because that the reviewers must sign their comments on the reviewed papers. The leakage of the reviewers' privacy may affect the judgement of the reviewers on the papers. In addition, the authors of a paper have to show their names to the editor of a conference proceedings or a journal when submitting the paper, so that it may also affect the decision of the editor on this paper. The major reason of the above problems is that the privacy or anonymity of the reviewers and the authors is not protected well, such that the reviewers and the editor cannot perform the reviewing processes without disturbance. In order to cope with the problems, we deeply analyze the privacy issue in the paper review system and then propose a generic idea, which is independent of the underlying cryptographic components, to achieve the anonymity property and other key requirements in a secure paper review scheme.

This thesis is concerned with the design and analysis of practical provably-secure encryption schemes. We give several results that include new schemes with attractive tradeoffs between efficiency and security and new techniques for analyzing existing schemes. Our results are divided into three chapters, which we summarize below. The Twin Diffie-Hellman Problem. We describe techniques for analyzing encryption schemes based on the hardness of Diffie-Hellman-type problems. We apply our techniques to several specific cases of encryption, including identity-based encryption, to design a collection of encryption schemes that offer improved tradeoffs between efficiency and evidence for security over similar schemes. In addition to offering quantitative advantages over prior work in this area, our technique also simplifies security proofs for these types of encryption schemes. Our main tool in this chapter is the notion of Twin Diffie-Hellman Problems, which provide an intermediate step for organizing security reductions and reveal very simple variants of known schemes with correspondingly simple, but non-obvious, analyses. Non-Malleable Hash Functions. We consider security proofs for encryption that are carried out in the random oracle model, where one declares that a scheme's hash functions are ``off limits' for an attacker in order to make a proof go through. Such proofs leave some doubt as to the security of the scheme in practice, when attackers are free to exploit weaknesses in the hash functions. A particular concern is that a scheme may be insecure in practice no matter what very strong security properties its real hash functions satisfy. We address this doubt for an encryption scheme of Bellare and Rogaway by showing that, using appropriately strong hash functions, this scheme's hash functions can be partially instantiated in a secure way.

Trapdoor functions, introduced in the seminal paper of Diffie and Hellman, are a fundamental notion in modern cryptography. Informally, trapdoor functions are injective functions that are easy to evaluate but hard to invert unless given an additional input called the trapdoor. Specifically, the classical security notion considered for trapdoor functions is one-wayness, which asks that it be hard to invert (except with very small probability) a uniformly random point in the range without the trapdoor. Motivated by the demands of emerging applications of cryptography as well as stronger security properties desired from higher-level cryptographic primitives constructed out of trapdoor functions, this thesis studies new strengthenings to the classical notion of one-way trapdoor functions and their applications. Our results are organized along two separate threads, wherein we introduce two new cryptographic primitives that strengthen the notion of one-wayness for trapdoor functions in different ways: Deterministic Encryption: Our notion of deterministic (public-key) encryption addresses the weaknesses of using trapdoor functions directly for encryption articulated by Goldwasser and Micali, to the extent possible without randomizing the encryption function (whereas Goldwasser and Micali address them using randomized encryption). Specifically, deterministic encryption ensures no partial information is leaked about a high-entropy plaintext or even multiple correlated such plaintexts. Deterministic encryption has applications to fast search on encrypted data, securing legacy protocols, and ``hedging' randomized encryption against bad randomness. We design a conceptually appealing semantic-security style definition of security for deterministic encryption as well as an easier-to-work-with but equivalent indistinguishability style definition. In the random oracle model of Bellare and Rogaway, we show a secure construction of deterministic encryption for an unbounded number of arbitrarily correlated high-entropy plaintexts based on any randomized encryption scheme, as well as length-preserving such construction based on RSA. In the standard model, we develop a general framework for constructing deterministic encryption schemes based on a new notion of ``robust' hardcore functions. We show a secure construction of deterministic for a single high-entropy plaintext based on exponentially-hard one-way trapdoor functions; single-message security is equivalent to security for an unbounded number of messages drawn from a block-source (where each subsequent message has high entropy conditioned on the previous). We also show a secure construction of deterministic encryption for a bounded number of arbitrarily correlated high-entropy plaintexts based on the notion of lossy trapdoor functions introduced by Peikert and Waters. paragraph*{Adaptive Trapdoor Functions:} Our notion of adaptive trapdoor functions asks that one-wayness be preserved in the presence of an inversion oracle that can be queried on some range points. The main application we give is the construction of black-box chosen-ciphertext secure public-key encryption from weaker general assumptions. (``Black-box' means that the specific code implementing the trapdoor function is not used in the construction, which typically incurs a huge efficiency cost.) Namely, we show such a construction of chosen-ciphertext secure public-key encryption from adaptive trapdoor functions. We then show that adaptive trapdoor functions can be realized from the recently introduced notions of lossy trapdoor functions by Peikert and Waters and correlated-product secure trapdoor functions by Rosen and Segev. In fact, by extending a recent result of Vahlis, we show adaptivity is strictly weaker than the latter notions (in a black-box sense). As a consequence, adaptivity is the weakest security property of trapdoor functions known to imply black-box chosen-ciphertext security. Additionally, by slightly extending our framework and considering ``tag-based' adaptive trapdoor functions, we obtain exactly the chosen-ciphertext secure encryption schemes proposed in prior work, thereby unifying them, although the schemes we obtain via adaptive trapdoor functions are actually more efficient. Finally, we show that adaptive trapdoor functions can be realized from a (non-standard) computational assumption on RSA inversion, leading to a very efficient RSA-based chosen-ciphertext secure encryption scheme in the standard model.